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ART. 388. -The Focal Date is the date from which the computation is begun in finding the equated time of the several debts and credits.
ART. 389.—To find the equated time where the
terms of credit begin at the same date.
A owes B $300 payable in 4 months; $500 payable in 6 months and $200 payable in 8 months: when should the whole be paid so that neither may lose ?
Analysis.-The interest on $300 for 4 300 x 4 = 1,200
months equals the interest on $1 for 500 x 6 = 3,000
1,200 months; the interest on $500 for 200 x 8 = 1,600
6 months equals that on $1 for 3,000
months, and the interest on $200 for 8 1,000 5,800 5,800 + 1,000 = 54.
months equals that on $1 for 1,600
months. Hence, the interest of the several amounts for the several periods equals the interest on $1 for 5,800 months, and on $1,000 it will be toto of 5,800 months = 54 months, which is the average term of credit from the date of the first indebtedness.
ART. 390.–Rule for finding the equated time, when the terms of credit begin on the same date.—Multiply each debt by its term of credit and divide the sum of the products by the sum of the payments.
NOTE.— Whenever cents appear in the debts, they should be rejected if less than 50 and counted as $1 if equal to or more than 50. If the Iraction of a day is less than 1, it is rejected, and if equal to or greater than ż, it is counted as 1 day.
2. Alexander Massey owed John Miller $4,000, # of which was due in 3 months, $ in 5 months, and the remainder in 8 months : what was the average term of credit ?
3. James Gardner owed a merchant $1,200, due in 3 months ; $900 due in 4 months; $800 due in 41 months : what was the average term of credit ?
4. John Spencer purchased a bill of goods, January 1, for $1,600. Of this amount, $400 was due in 1 month, $800 due in 3 months, and $400 due in 6 months : what was the average term of credit ?
5. A merchant owed $3,000, of which was due in 3} months, } in 4 months, and ž in 6 months : find the equated time of payment.
6. Mr. Graham's debt of $10,000 was due as follows: ☆ in 41 months, in 5 months, and fin y months : what was the equated time ?
7. Mr. Braham owed $1,500.75 due in 10 days ; $300.50 due in 15 days; $800.25 due in 20 days : what was the average term of credit ?
8. Illustrate Art. 389 by an original problem.
ART. 391.-To find the equated time, when the
terms of credit begin on different dates.
1. A merchant laid in a supply of goods as follows:
If these bills were all paid at once, on what day should such payment have been made ?
Analysis.—84,900 = 1,900 April 1, 800 00 = 00,000 = 44,5, or 44 days, from May 25, 600 x
54 = 32,400 April 1 (when the first payJuly 15, 500 x 105 = 52,500 ment was due), which makes 1,900
the equated time May 15.
ART. 392.-Rule for finding the equated time when the terms of credit begin on different dates. —Take as the focal date the date on which the first debt becomes due, and multiply each debt by the term of credit, reckoned from that date. The sum of these products, divided by the sum of the debts, is the average term of credit, reckoned from the focal date.
2. Mr. Smith bought, Feb. 10, $500 worth of goods on 3 months' credit; March 20, $450 on 3 months' credit; April 10, $600 on 4 months' credit; May 15, $800 on 4 months' credit: what was the equated time of payment ?
3. Mr. Brown bought a bill of goods, on March 20 on 6 months' credit, amounting to $40; March 25 a bill on 4 months' credit, amounting to $30; April 24, on 6 months' credit, a bill of $30; June 17, on 3 months' credit, a bill of $50: what was the equated time of payment ?
4. Illustrate Art. 391 by an original problem.
of finding the average time for the payment of the balance of an account.
What is the equated time for the payment of the balance ?
Process. We take as the focal date the earliest date on which any item on either side matures. The latest date, or a date intermediate between the earliest and the latest, may be taken as the focal date, but the earliest is most convenient.
Analysis.-By the process already explained we find that the items on the Dr. side are entitled to the discount of $1 for 53,000 days, while those on the Cr. side are entitled to a discount of $1 for 22,500 days. The difference shows the Dr. side entitled to the discount of $1 for 30,500 days, and $300 therefore is entitled to do of 30,500 days, or 102 days. Hence, the balance is due in 102 days after June 1, which is September 11.
ART. 394.-Rule for averaging accounts.--Take as the focal date the date when the first payment is due, and multiply each item by the number of days it falls due after the focal date. Multiply also the amount of each payment by the number of days it is made after the focal date.
The difference between these respective products, divided by the difference between the columns of items gives a quotient, which, added to the focal date, is the equated time
If the balances are on opposite sides of the account, the quotient must be subtracted from the focal date.